Question

At a certain dinner party, ten guests are to be seated around a circular table. How many different arrangements are possidble? (Two arrangements are considered the same if each guest is seated between the same people.)

Answer 1

@amistre64

Answer 2

the circle one has always thrown me, but i believe the adjustment is similar to combination.

Answer 3

10 ways for the first seat, 9 for the next, 8,7,6,5,4,3,2,1

and each arrangement can be resat 10 times due to a shift in seating

Answer 4

(1,2) = (2,1)

2!/2 = 1!
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(1,2,3) = (2,3,1) = (3,1,2)
(1,3,2) = (2,1,3) = (3,2,1)

3!/3 = 2!
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(1,2,3,4) = (2,3,4,1) = (3,4,1,2) = (4,1,2,3)
(1,2,4,3) = (2,4,3,1) = (3,1,2,4) = (4,3,1,2)
(1,3,4,2) = (2,1,3,4) = (3,4,2,1) = (4,2,1,3)
(1,3,2,4) = (2,4,1,3) = (3,2,4,1) = (4,1,3,2)
(1,4,2,3) = (2,3,1,4) = (3,1,4,2) = (4,2,3,1)
(1,4,3,2) = (2,1,4,3) = (3,2,1,4) = (4,3,2,1)

4!/4 = 3!

seems to suggest a pattern of events eh